Research On Algorithms For Equilibrium And Non-equilibrium Traffic Assignment Models

Traffic flow assignment is a basic problem of city traffic's program and government. It also is an important study field of applied mathematics.Firstly, some basic concepts and properties about traffic assignment problem are presented in this thesis, it includes typic equilibrium models and non-equilibrium assignment methods.Secondly, this thesis mainly studies the new method to solve User's Equilibrium model with fixed demand in traffic assignment problem. According to the link capacity, this kind of problem can be fell into two traffic assignment problems with and without link capacity limit. At first, we point out that the optimal solution of the model with link capacity constraints satisfy Wardrop's first principle. Given proper link impedance function, two kinds of problems can be united for one same-formed nonlinear program problem with linear constrains. To solve this problem, this paper firstly adopts gradient projection algorithm with affine scaling in interior -point methods, and gives it's general idea, iterated steps and detail implementation process. One small traffic assignment problem is solved by this algorithm. The computational results show that this method is effective and efficient. Especially, because the computational quantity of interior-point methods is not so sensitive to problem's scale, the given method can be used to the traffic flow assignments in reality large and middle road networks.Lastly, the paper also proposes one algorithm of non-equilibrium traffic assignment. It is the shortest path-Logit assignment method in turn. After being divided the OD table into m same parts, the algorithm includes two steps. In the first step, we mainly combine the shortest path algorithm with Logit model to search the better path of each OD pair, which we name "the shortest path" set. And in the second step, adopting Logit model, we add all the OD sub-tables to these "shortest" paths in turn. This algorithm replaces path enumeration by searching the shortest path in road network, so it is a reasonable improvement of Logit random assignment method, and is suit to the flow assignment in reality network.